Solve 4(3y-7)^2=1

$$4 ( 3 y - 7 ) ^ { 2 } = 1$$

Solve for y

$$y = \frac{5}{2} = 2\frac{1}{2} = 2.5$$

$$y = \frac{13}{6} = 2\frac{1}{6} \approx 2.166666667$$

Steps by Finding Square Root

Divide both sides by 4.

$$\frac{4\left(3y-7\right)^{2}}{4}=\frac{1}{4}$$

Dividing by 4 undoes the multiplication by 4.

$$\left(3y-7\right)^{2}=\frac{1}{4}$$

Take the square root of both sides of the equation.

$$3y-7=\frac{1}{2} 3y-7=-\frac{1}{2}$$

Add 7 to both sides of the equation.

$$3y-7-\left(-7\right)=\frac{1}{2}-\left(-7\right) 3y-7-\left(-7\right)=-\frac{1}{2}-\left(-7\right)$$

Subtracting -7 from itself leaves 0.

$$3y=\frac{1}{2}-\left(-7\right) 3y=-\frac{1}{2}-\left(-7\right)$$

Subtract -7 from \frac{1}{2}.

$$3y=\frac{15}{2}$$

Subtract -7 from -\frac{1}{2}.

$$3y=\frac{13}{2}$$

Divide both sides by 3.

$$\frac{3y}{3}=\frac{\frac{15}{2}}{3} \frac{3y}{3}=\frac{\frac{13}{2}}{3}$$

Dividing by 3 undoes the multiplication by 3.

$$y=\frac{\frac{15}{2}}{3} y=\frac{\frac{13}{2}}{3}$$

Divide \frac{15}{2} by 3.

$$y=\frac{5}{2}$$

Divide \frac{13}{2} by 3.

$$y=\frac{13}{6}$$

The equation is now solved.

$$y=\frac{5}{2} y=\frac{13}{6}$$